The tags and categories created in different servers will be available for all servers which is the **expected behavior**, at the moment. This is because the catalog management elements (tags, property groups, categories) are **global for all the servers**.
However, the views or web service objects with associated categories or tags (or other elements) are independent of each server. (i.e relations of tags and categories to a view or web service object is specific to a server configuration)
For more information, you could refer to the [Catalog Management](https://community.denodo.com/docs/html/browse/latest/en/vdp/data_catalog/administration/catalog_management/catalog_management) sections of the Data Catalog Guide.
Hope this helps!